The 29-year-old midfielder made 48 appearances during his 12-month stint at Stamford Bridge, winning both the FA Cup and Champions League.
Whilst he missed the Champions League final due to suspension after receiving a booking at Camp Nou in the semi-final second-leg, he still received a medal, and was full of praise for his time in west London.
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"I came to say goodbye to my friends and of course I will miss this club and the fans and the city," he told Chelsea's official website.
"There are some great people here, they always supported me and they help everyone, so of course I had to come to say goodbye to everyone."Meireles joined Chelsea for a fee of around €15 million from Premier League rivals Liverpool and fired Roberto Di Matteo's side to the semi-final of the Champions League with a goal against Benfica.
But he was deemed surplus to requirements following the arrival of Eden Hazard and Brazilian youngster Oscar this summer and said that he is now looking forward to a new challenge with a new club.
"It was a great year," he added.
"The last part of the season was great, we won the Champions League, the FA Cup, and it was very good for me. I will miss these moments but it is a new challenge for me and I am ready to go to Turkey.
"I hope things go well for me like they did at Chelsea this year. I have been to Fenerbahce just to sign and tomorrow is my first day and I am excited to start.
"Thanks to the fans for their support and I will miss this club a lot, it was very nice to play for Chelsea."